Mathematics Question Thread

[Thebarman]

How would I go about answering this question? Thanks

[Shadowxo]

How would I go about answering this question? Thanks

Hi
I don't know what method they'd like you to use for this, so have you been taught either
1) integration by parts or
2) using a function like e^x to find the area?

[georgiia]

I am slightly confused by this question, is it asking for growth in rate or growth in population because if it's population growth, there isn't enough information provided so

Thank you

[Shadowxo]

I believe it's asking for the change in population. Since you're given the rate of change of population (ie dP/dt where P is population) you should be able to find the change in population by finding the integral between 1 and 3 of R(t) 

[RuiAce]

Hi
I don't know what method they'd like you to use for this, so have you been taught either
1) integration by parts or
2) using a function like e^x to find the area?

Show them the latter please; IBP is for MX2

[georgiia]

I believe it's asking for the change in population. Since you're given the rate of change of population (ie dP/dt where P is population) you should be able to find the change in population by finding the integral between 1 and 3 of R(t) 

Ahh! Didn't think of attaching limits to the integral
I was stuck with a C I couldn't find

Thx

[georgiia]

My working is in black and the answer provided is pink. Would I still get the mark for failing to see if the quicker way of answering the question?

Thanks

[georgiia]

My working is in black and the answer provided is pink. Would I still get the mark for failing to see if the quicker way of answering the question?

Thanks

[Shadowxo]

Show them the latter please; IBP is for MX2

Thought so but wasn't sure

How would I go about answering this question? Thanks

So finding the integral of ln(x) is difficult, but finding the integral of e^x is easy. e^x and ln(x) are inverse functions of each other (if you don't know this or are given a more complicated question, you can figure it out by finding the inverse function like usual).
In this kind of question, a diagram is useful I'll attach my working/solution

My working is in black and the answer provided is pink. Would I still get the mark for failing to see if the quicker way of answering the question?

Thanks

I think your method is valid but since it asks how you know the population is decreasing, rather than asking what will happen to the population, it would probably be safer to find dp/dt and hence show it's less than 0, ie decreasing

[georgiia]

Thought so but wasn't sure
So finding the integral of ln(x) is difficult, but finding the integral of e^x is easy. e^x and ln(x) are inverse functions of each other (if you don't know this or are given a more complicated question, you can figure it out by finding the inverse function like usual).
In this kind of question, a diagram is useful I'll attach my working/solution(Image removed from quote.)
I think your method is valid but since it asks how you know the population is decreasing, rather than asking what will happen to the population, it would probably be safer to find dp/dt and hence show it's less than 0, ie decreasing

Thanks, yeah that makes sense

[georgiia]

I just have a clarification question here:

(For iii.)

Because I get two answers, is it safe to just ignore t=75 because of the fact that it takes him t=50 to empty the contents thus I can assume that t=75 is inadmissible even if they didn't supply a domain in the Q. ?

[Shadowxo]

I just have a clarification question here:

(For iii.)

Because I get two answers, is it safe to just ignore t=75 because of the fact that it takes him t=50 to empty the contents thus I can assume that t=75 is inadmissible even if they didn't supply a domain in the Q. ?

Can't see the question, did you attach it properly?

[mlarsson]

Hey just wanted to confirm a few things, because my teacher hasnt been very clear about this topic. How do you know when to use logs in an equation ? (besides the questions where it is obviously asking about logs?)

[georgiia]

Hey just wanted to confirm a few things, because my teacher hasnt been very clear about this topic. How do you know when to use logs in an equation ? (besides the questions where it is obviously asking about logs?)

When the unknown is to the power of e

Like this:

e^t=5

Ln(e)^t=ln(5)

t=ln(5)

[georgiia]

Can't see the question, did you attach it properly?

Fixed it